516. Longest Palindromic Subsequence
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题目:
Given a string s, find the longest palindromic subsequence's length in s. You may assume that the maximum length of s is 1000.
Example 1:
Input:
"bbbab"Output:
4One possible longest palindromic subsequence is "bbbb".
Example 2:
Input:
"cbbd"Output:
2One possible longest palindromic subsequence is "bb".
思路:用动态规划的方法,令longest[i][j]表示字符串中从第i为到第j位的子字符串中最长的回文的长度,
if i==j longest[i][j] = 0;
if i+1 == j, then longest[i][j] = 2 if s[i] == s[j] longest[i][j] = 1
otherwise
if s[i] == s[j] dp[i][j] = max(dp[i+1][j], dp[i][j-1], dp[i+1][j-1] + 2)
if s[i] != s[j] dp[i][j] = max(dp[i+1][j], dp[i][j-1], dp[i+1][j-1])
return longest[0][s.size()]
复杂度为O(n^2)
代码:
class Solution {
public:
int longestPalindromeSubseq(string s) {
if(s.size() == 0)
{
return 0;
}
vector<vector<int>> longest(s.size(), vector<int>(s.size()));
for(int k = 1;k<=s.size();k++)
{
for(int i = 0;i+k<=s.size();i++)
{
int j = i+k-1;
if(i == j)
{
longest[i][j] = 1;
}
else if(i+1 == j)
{
longest[i][j] = (s[i] == s[j]) ? 2:1;
}
else
{
int temp = s[i] == s[j]? 2 : 0;
longest[i][j] = max(max(longest[i][j-1], longest[i+1][j]), longest[i+1][j-1] + temp);
}
}
}
return longest[0][s.size()-1];
}
};
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
- 516. Longest Palindromic Subsequence
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